Application of multivariate bilinear neural network method to fractional partial differential equations

Abstract

In this work, a multivariate bilinear neural network method is proposed to seek more exact analytical solutions of nonlinear partial differential equations. As an example, the (2+1)-dimensional fractional generalized Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–Konopelchenko equation is investigated via selecting the 3-2-2-1, 3-2-3-1 and 3-3-2-1 models, respectively. The exact analytical solutions with several arbitrary activation functions are derived and the dynamics properties are shown in some three-dimensional and density maps by choosing different activation functions.

Keywords

• Multivariate bilinear neural network method
• Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–Konopelchenko equation
• Fractional